Usage of SDP Relaxation in Some GNSS Navigation Problems

Abstract

In this paper, we propose an approach to the solution of two optimization problems that arise when solving problems of satellite navigation. The first problem consists in attitude determination using carrier phase and code range observables measured by multiple GNSS antennas. In general, the attitude determination is the non-convex optimization problem. The second problem consists in the optimization of the set of the Global Navigation Satellite System (GNSS) signals chosen for processing when solving the positioning problem. It is the binary optimization problem which is hard for a solution in real time. We show how these problems can be reduced to the convex semidefinite programming problem (SDP) and, therefore, efficiently solved.